The structure of Neoprene is -
Question: The structure of Neoprene is -Correct Option: , 3 Solution:...
Read More →1 molar aqueous solution
Question: 1 molar aqueous solution of an electrolyte $\mathrm{A}_{2} \mathrm{~B}_{3}$ is $60 \%$ ionised. The boiling point of the solution at $1 \mathrm{~atm}$ is__________K. (Rounded-off to the nearest integer) $\left[\right.$ Given $\mathrm{K}_{\mathrm{b}}$ for $\left.\left(\mathrm{H}_{2} \mathrm{O}\right)=0.52 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\right]$ Solution: $\Delta \mathrm{T}_{\mathrm{b}}=\mathrm{iK}_{\mathrm{b}} \mathrm{m}$ $=(1+4 \alpha) \times 0.52 \times 1$ $=3.4 \times 0.5...
Read More →A possible value of
Question: A possible value of ' $x$ ', for which the ninth term in the expansion of $\left\{3^{\log _{3} \sqrt{25^{x-1}+7}}+3^{\left(-\frac{1}{8}\right) \log _{3}\left(5^{x-1}+1\right)}\right\}^{10}$ in the increasing powers of $3^{\left(-\frac{1}{8}\right) \log _{3}\left(5^{x-1}+1\right)}$ is equal to 180 , is : 0$-1$21Correct Option: , 4 Solution: ${ }^{10} \mathrm{C}_{8}\left(25^{(\mathrm{x}-1)}+7\right) \times\left(5^{(\mathrm{x}-1)}+1\right)^{-1}=180$ $\Rightarrow \frac{25^{x-1}+7}{5^{(x-1)...
Read More →Among the following,
Question: Among the following, the number of halide(s) which is/are inert to hydrolysis is$\mathrm{BF}_{3}$$\mathrm{SiCl}_{4}$$\mathrm{PCl}_{5}$$\mathrm{SF}_{6}$Correct Option: 1 Solution: $\mathrm{SF}_{6}$ is inert towards hydrolysis $\therefore$ answere is (1)...
Read More →Which of the following reagent is used for the following reaction ?
Question: Which of the following reagent is used for the following reaction ? $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{3} \stackrel{?}{\longrightarrow} \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CHO}$Manganese acetateCopper at high temperature and pressureMolybdenum oxidePotassium permanganateCorrect Option: , 3 Solution: $\mathrm{CH}_{3}-\mathrm{CH}_{2}-\mathrm{CH}_{3} \stackrel{\mathrm{MO}_{2} \mathrm{O}_{3}}{\longrightarrow} \mathrm{CH}_{3}-\mathrm{CH}_{2}-\mathrm{CH}=\mathrm{O}$ The reagen...
Read More →Solve this following
Question: The point $P(a, b)$ undergoes the following three transformations successively : (a) reflection about the line $y=x$. (b) translation through 2 units along the positive direction of $\mathrm{x}$-axis. (c) rotation through angle $\frac{\pi}{4}$ about the origin in the anti-clockwise direction. If the co-ordinates of the final position of the point $P$ are $\left(-\frac{1}{\sqrt{2}}, \frac{7}{\sqrt{2}}\right)$, then the value of $2 a+b$ is equal to : 13957Correct Option: , 2 Solution: Im...
Read More →The major product of the following chemical reaction is :
Question: The major product of the following chemical reaction is : $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{3}$$\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{OH}$$\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CO}\right)_{2} \mathrm{O}$$\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CHO}$Correct Option: , 4 Solution: Final product of reaction is propanaldehyde....
Read More →If the lines
Question: If the lines $\frac{x-k}{1}=\frac{y-2}{2}=\frac{z-3}{3}$ and $\frac{x+1}{3}=\frac{y+2}{2}=\frac{z+3}{1}$ are co-planar, then the value of $\mathrm{k}$ is________. Solution: $\left|\begin{array}{ccc}\mathrm{k}+1 4 6 \\ 1 2 3 \\ 3 2 1\end{array}\right|=0$ $(k+1)[2-6]-4[1-9]+6[2-6]=0$ $\mathrm{k}=1$...
Read More →Which statement is correct?
Question: Which statement is correct?Synthesis of Buna-S needs nascent oxygen.Neoprene is an addition copolymer used in plastic bucket manufacturing.Buna-S is a synthetic and linear thermosetting polymer.Buna- $\mathrm{N}$ is a natural polymer.Correct Option: 1 Solution:...
Read More →If the co-efficient of
Question: If the co-efficient of $x^{7}$ and $x^{8}$ in the expansion of $\left(2+\frac{x}{3}\right)^{n}$ are equal, then the value of $n$ is equal to________. Solution: ${ }^{n} C_{7} 2^{n-7} \frac{1}{3^{7}}={ }^{n} C_{8} 2^{n-8} \frac{1}{3^{8}}$ $\Rightarrow \mathrm{n}-7=48 \Rightarrow \mathrm{n}=55$...
Read More →What is the major product formed by HI on
Question: What is the major product formed by HI on Correct Option: , 3 Solution:...
Read More →A fair coin is tossed n-times such that the probability
Question: A fair coin is tossed n-times such that the probability of getting at least one head is at least 0.9. Then the minimum value of $\mathrm{n}$ is_________. Solution: $\mathrm{P}($ Head $)=\frac{1}{2}$ $1-\mathrm{P}($ All tail $) \geq 0.9$ $1-\left(\frac{1}{2}\right)^{\mathrm{n}} \geq 0.9$ $\Rightarrow\left(\frac{1}{2}\right)^{\mathrm{n}} \leq \frac{1}{10}$ $\Rightarrow \mathrm{n}_{\min }=4$...
Read More →If a+b+c=1, a b+b c+c a=2 and a b c=3,
Question: If $a+b+c=1, a b+b c+c a=2$ and $a b c=3$, then the value of $a^{4}+b^{4}+c^{4}$ is equal to Solution: $a^{2}+b^{2}+c^{2}=(a+b+c)^{2}-2 \Sigma a b=-3$ $(a b+b c+c a)^{2}=\Sigma(a b)^{2}+2 a b c \Sigma a$ $\Rightarrow \Sigma(a b)^{2}=-2$ $a^{4}+b^{4}+c^{4}=\left(a^{2}+b^{2}+c^{2}\right)^{2}-2 \Sigma(a b)^{2}$ $=9-2(-2)=13$...
Read More →In Freundlich adsorption isotherm
Question: In Freundlich adsorption isotherm at moderate pressure, the extent of adsorption $\left(\frac{x}{m}\right)$ is directly proportional to $P^{x}$. The value of $x$ isZero$\frac{1}{\mathrm{n}}$1$\infty$Correct Option: , 2 Solution: As per Freundlich adsorption isotherm $\left(\frac{x}{m}\right)=K P^{\frac{1}{n}} \rightarrow x=\frac{1}{n}$ Hence answer is (2)...
Read More →Let a curve y=f(x) pass through the point
Question: Let a curve $y=f(x)$ pass through the point $\left(2,\left(\log _{e} 2\right)^{2}\right)$ and have slope $\frac{2 y}{x \log _{e} x}$ for all positive real value of $x$. Then the value of $f(e)$ is equal to Solution: $y^{\prime}=\frac{2 y}{x \ell n x}$ $\Rightarrow \frac{\mathrm{dy}}{\mathrm{y}}=\frac{2 \mathrm{dx}}{\mathrm{x} \ell \mathrm{nx}}$ $\Rightarrow \ell \mathrm{n}|\mathrm{y}|=2 \ell \mathrm{n}|\ell \mathrm{nx}|+\mathrm{C}$ put $x=2, y=(\ell n 2)^{2}$ $\Rightarrow \mathrm{c}=0$...
Read More →The solubility of
Question: The solubility of $\mathrm{AgCN}$ in a buffer solution of $\mathrm{pH}=3$ is $\mathrm{x}$. The value of $\mathrm{x}$ is: [Assume: No cyano complex is formed; $\mathrm{K}_{\mathrm{sp}}(\mathrm{AgCN})$ $=2.2 \times 10^{-16}$ and $\mathrm{K}_{\mathrm{a}}(\mathrm{HCN})=6.2 \times 10^{-10}$ ]$0.625 \times 10^{-6}$$1.9 \times 10^{-5}$$2.2 \times 10^{-16}$$1.6 \times 10^{-6}$Correct Option: , 2 Solution: $\frac{\mathrm{K}_{\mathrm{sp}}}{\mathrm{Ka}}=\frac{\mathrm{s}^{2}}{\left(\mathrm{H}^{+}\...
Read More →Prove the following
Question: If $(\vec{a}+3 \vec{b})$ is perpendicular to $(7 \vec{a}-5 \vec{b})$ and $(\vec{a}-4 \vec{b})$ is perpendicular to $(7 \vec{a}-2 \vec{b})$, then the angle between $\overrightarrow{\mathrm{a}}$ and $\overrightarrow{\mathrm{b}}$ (in degrees) is_______. Solution: $(\vec{a}+3 \vec{b}) \perp(7 \vec{a}-5 \vec{b})$ $(\vec{a}+3 \vec{b}) \cdot(7 \vec{a}-5 \vec{b})=0$ $7|\vec{a}|^{2}-15|\vec{b}|^{2}+16 \vec{a} \cdot \vec{b}=0$............(1) $(\vec{a}-4 \vec{b}) \cdot(7 \vec{a}-2 \vec{b})=0$ $7|...
Read More →Solve this
Question: (A) $\mathrm{HOCl}+\mathrm{H}_{2} \mathrm{O}_{2} \rightarrow \mathrm{H}_{3} \mathrm{O}^{+}+\mathrm{Cl}^{-}+\mathrm{O}_{2}$ (B) $\mathrm{I}_{2}+\mathrm{H}_{2} \mathrm{O}_{2}+2 \mathrm{OH}^{-} \rightarrow 2 \mathrm{I}^{-}+2 \mathrm{H}_{2} \mathrm{O}+\mathrm{O}_{2}$ (A) $\mathrm{HOCl}+\mathrm{H}_{2} \mathrm{O}_{2} \rightarrow \mathrm{H}_{3} \mathrm{O}^{+}+\mathrm{Cl}^{-}+\mathrm{O}_{2}$ In this equation, $\mathrm{H}_{2} \mathrm{O}_{2}$ is reducing chlorine from $+1$ to $-1$. (B) $\mathrm{...
Read More →Solve this following
Question: Let $\mathrm{f}:[0,3] \rightarrow \mathbf{R}$ be defined by $f(x)=\min \{x-[x], 1+[x]-x\}$ where $[x]$ is the greatest integer less than or equal to $x$. Let $P$ denote the set containing all $x \in[0,3]$ where $\mathrm{f}$ is discontinuous, and $\mathrm{Q}$ denote the set containing all $x \in(0,3)$ where $f$ is not differentiable. Then the sum of number of elements in $P$ and $Q$ is equal to Solution: $1-\{x\}=1-x ; 0 \leq x1$ Non differentiable at $x=\frac{1}{2}, 1, \frac{3}{2}, 2, ...
Read More →Ellingham diagram is a graphical representation of:
Question: Ellingham diagram is a graphical representation of:$\Delta \mathrm{H}$ vs $\mathrm{T}$$\Delta \mathrm{G}$ vs $\mathrm{T}$$\Delta G$ vs $P$$(\Delta \mathrm{G}-\mathrm{T} \Delta \mathrm{S})$ vs $\mathrm{T}$Correct Option: , 2 Solution: Ellingham diagram is a graphical representation of $\Delta \mathrm{G}$ vs $\mathrm{T}$ when metal heated with oxygen to form metal oxide...
Read More →If a rectangle is inscribed in an equilateral triangle of side
Question: If a rectangle is inscribed in an equilateral triangle of side length $2 \sqrt{2}$ as shown in the figure, then the square of the largest area of such a rectangle is__________. Solution: In $\triangle \mathrm{DBF}$ $\tan 60^{\circ}=\frac{2 b}{2 \sqrt{2}-\ell} \Rightarrow b=\frac{\sqrt{3}(2 \sqrt{2}-\ell)}{2}$ $\mathrm{A}=$ Area of rectangle $=\ell \times \mathrm{b}$ $A=\ell \times \frac{\sqrt{3}}{2}(2 \sqrt{2}-\ell)$ $\frac{\mathrm{d} \mathrm{A}}{\mathrm{d} \ell}=\frac{\sqrt{3}}{2}(2 \...
Read More →The hybridization and magnetic nature
Question: The hybridization and magnetic nature of $\left[\mathrm{Mn}(\mathrm{CN})_{6}\right]^{4}$ and $\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}$, respectively are:$\mathrm{d}^{2} \mathrm{sp}^{3}$ and diamagnetic$\mathrm{sp}^{3} \mathrm{~d}^{2}$ and diamagnetic$\mathrm{d}^{2} \mathrm{sp}^{3}$ and paramagnetic$\mathrm{sp}^{3} \mathrm{~d}^{2}$ and paramagneticCorrect Option: , 3 Solution: $\therefore$ hybridisation is $\mathrm{d}^{2} \mathrm{sp}^{3}$ and due to presence of unpaired $e^{-}$co...
Read More →Solve this following
Question: If $y=y(x), \quad y \in\left[0, \frac{\pi}{2}\right)$ is the solution of the differential equation $\sec y \frac{d y}{d x}-\sin (x+y)-\sin (x-y)=0$, with $y(0)=0$ then $5 \mathrm{y}^{\prime}\left(\frac{\pi}{2}\right)$ is equal to Solution: $\sec y \frac{d y}{d x}=2 \sin x \cos y$ $\sec ^{2} y d y=2 \sin x d x$ $\tan y=-2 \cos x+c$ $c=2$ $\tan y=-2 \cos x+2 \Rightarrow$ at $x=\frac{\pi}{2}$ $\tan y=2$ $\sec ^{2} y \frac{d y}{d x}=2 \sin x$ $5 \frac{\mathrm{dy}}{\mathrm{dx}}=2$...
Read More →The equation of a circle is
Question: The equation of a circle is $\operatorname{Re}\left(z^{2}\right)+2(\operatorname{Im}(z))^{2}+2 \operatorname{Re}(z)=0$, where $z=x+i y$. A line which passes through the center of the given circle and the vertex of the parabola, $x^{2}-6 x-y+13=0$, has $y$-intercept equal to_______. Solution: Equation of circle is $\left(x^{2}-y^{2}\right)+2 y^{2}+2 x=0$ $x^{2}+y^{2}+2 x=0$ Centre: $(-1,0)$ Parabola : $x^{2}-6 x-y+13=0$ $(x-3)^{2}=y-4$ Vertex : $(3,4)$ Equation of line $\equiv y-0=\frac...
Read More →In Freundlich adsorption isotherm, slope of AB line is :
Question: In Freundlich adsorption isotherm, slope of AB line is : $\log n$ with $(n1)$$\mathrm{n}$ with $(\mathrm{n}, 0.1$ to $0.5)$$\log \frac{1}{n}$ with $(n1)$$\frac{1}{\mathrm{n}}$ with $\left(\frac{1}{\mathrm{n}}=0\right.$ to 1$)$Correct Option: , 4 Solution: $\frac{x}{m}=K(P)^{1 / n}$ $\log \left(\frac{x}{m}\right)=\log K+\frac{1}{n} \log P$ $y=c+m x$ $\mathrm{m}=1 / \mathrm{n}$ so slope will be equal to $1 / \mathrm{n}$....
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